Elements of Plane and Spherical TrigonometryBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 2
... three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other three ; when it is possible . II . Knowing three of the six things which compose a triangle formed on ...
... three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other three ; when it is possible . II . Knowing three of the six things which compose a triangle formed on ...
Página 3
... three angles of a triangle remain the same , the sides , though retaining the same mutual relation , may be greater or less , in all conceivable proportions . 7. Lemma I. Let ACB be a rectilinear angle : if , about the point c as a ...
... three angles of a triangle remain the same , the sides , though retaining the same mutual relation , may be greater or less , in all conceivable proportions . 7. Lemma I. Let ACB be a rectilinear angle : if , about the point c as a ...
Página 11
... three angles of the triangle ABC are equal , and therefore the triangle is equilateral . Conseq . AB = radius . B T D A 2. CD = DA CA , because in an isosceles or equi- lateral triangle the perp . bisects the base . 3 ... sides AT , and AC ...
... three angles of the triangle ABC are equal , and therefore the triangle is equilateral . Conseq . AB = radius . B T D A 2. CD = DA CA , because in an isosceles or equi- lateral triangle the perp . bisects the base . 3 ... sides AT , and AC ...
Página 24
... three sides and three angles , of which some three are given to determine the other three ; and the combinations that can be formed out of six quantities , taken three and three being = 6.5.4 1.2.3 or 20 ; it might at first sight be ...
... three sides and three angles , of which some three are given to determine the other three ; and the combinations that can be formed out of six quantities , taken three and three being = 6.5.4 1.2.3 or 20 ; it might at first sight be ...
Página 25
... sides respec- tively opposite ; then the twenty varieties of data will be these , viz . ( 3 ) abc ... ( 1 ) aba ... three , indicated by the number 2 , have this in common , that two sides and an included angle are given ; they ...
... sides respec- tively opposite ; then the twenty varieties of data will be these , viz . ( 3 ) abc ... ( 1 ) aba ... three , indicated by the number 2 , have this in common , that two sides and an included angle are given ; they ...
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Términos y frases comunes
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius rectangle right angled spherical right angled triangle right ascension right line secant sin a sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence yards zenith
Pasajes populares
Página 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Página 248 - SCIENTIFIC DIALOGUES ; intended for the Instruction and Entertainment of Young People ; in which the first principles of Natural and Experimental Philosophy are fully explained, by the Rev.
Página 225 - ... third of the excess of the sum of its three angles above two right angles...
Página 19 - In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Página 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 249 - OSTELL'S NEW GENERAL ATLAS; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Página 34 - Call any one of the sides radius, and write upon it the word radius ; observe whether the other sides become sines, tangents, or secants, and write those words upon them accordingly. Call the word written upon each side the name of each side ; then say, As the name of the given side, Is to the given side ; So is the name of the required side, To the required side.
Página 69 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Página 18 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Página 83 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...